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arXiv · 1407.8081

On the momentum of solitons and vortex rings in a superfluid

L. P. Pitaevskii
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Abstract

This paper is devoted to the calculation of the momentum of localized excitations, such as solitons and vortex rings, moving in a superfluid. The direct calculation of the momentum by integration of the mass flux density results in a badly-converging integral. I suggest a method for the renormalization of the integral with the explicit separation of a term related to the vortex line. This term can be calculated explicitly and gives the main contribution for the rings whose size is large compared to the healing length. I compare my method with the Jones and Roberts prescription for the renormalization. I investigate the case of a uniform superfluid, and that of a superfluid in a cylindrical trap. I discuss the calculation of the jump in the phase of the order parameter and obtain a simple estimate for this jump for a large ring in the trap.

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L. P. Pitaevskii. 2014-07-30. On the momentum of solitons and vortex rings in a superfluid. https://doi.org/10.1134/s1063776114120152

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